Sen. Marco Rubio (R-Fla.) believes that the immigration bill he helped write will eventually get enough votes to break a filibuster in the Senate.

Earlier this week, Rubio cast doubt on the bill's ability to pass the Senate, saying that the border security language was not tough enough to attract a sufficient number of Republican votes. The Florida senator even said he might vote against his own bill if changes are not made. That prompted questions over Rubio's commitment to passing the legislation.

During a Univision interview, Rubio said that the bill's authors have not yet rounded up 60 votes -- enough to prevent it from being filibustered by its opponents. But he said that he is "100 percent committed to the immigration issue" and that he wants tougher border measures in order to "earn our colleagues' trust," and not to kill the bill.

"We'll have a lot more than 60 votes, but we're going to have to work at it," he told Univision's Maria Elena Salinas in an interview that will air Sunday on "Al Punto."

Formal debate on the bill began on the Senate floor on Friday. Rubio's optimistic tone comes after immigrant-rights activists voiced concern that the senator's comments about the bill's potential failure could stunt its momentum as it heads toward a vote in the Senate.

And activists aren't pleased that Rubio wants to add additional border measures to a bill the senator previously described as the toughest enforcement bill in U.S. history. Protesters conducted a sit-in at Rubio's office in Miami on Thursday over proposed changes to the border security elements of the legislation.

But Rubio told Univision that his GOP colleagues are willing to bend on their rejection of a path to citizenship if the border-security measures are sound.

"Many colleagues who just four or five years ago were not in favor of granting legal status to the people who were here illegally, who were not in favor of creating a path to citizenship, today are open to it," he said. "They're simply asking that we make sure that the border is secure and that another wave of illegal migration doesn't take place in the future."